The generalised Ramsey number R(G1, G2,..., Gk) is defined as the smallest integer n such that, if the edges of Kn, the complete graph on n vertices, are coloured using k colours C1, C2,..., Ck, then for some i(1≤i≤k) there is a subgraph Gi of Kn with all of its edges colour Ci.
The Ramsey number r=r(G1-G2-⋯-Gm,H1-H2-⋯-Hn) denotes the smallest r such that every 2-coloring of the edges of the complete graph Kr contains a subgraph Gi ...
May 2, 2023 · The Ramsey number describes how many nodes a complete graph must contain to be forced to have a particular structure. Say the edges of a ...
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ABSTRACT: We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph,.
For a graph G, n(G) and e(G) denote the number of vertices and edges, respectively, in G. Section 2 contains the data for the classical two color Ramsey numbers ...
In the language of graph theory, the Ramsey number is the minimum number of vertices, v = R(m, n), such that all undirected simple graphs of order v, contain a ...
Abstract: Let R(G) denote the minimum integer N such that for every bicoloring of the edges of KN, at least one of the monochromatic subgraphs.
The Ramsey number r(G, H) is determined for all disconnected (isolate- free) graphs H of order six and all graphs G of order at most five, except.
We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, multicolor and hypergraph Ramsey ...
Oct 22, 2024 · These Ramsey numbers are determined for all sets of graphs with at most four vertices, and in the diagonal case (m=n, Gi=Hi) for all pairs of ...